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Chapter 11: Problem 12

To make a goodness-of-fit test, what should be the minimum expected frequency for each category? What are the alternatives if this condition is not satisfied?

Short Answer

Expert verified
For each category in a goodness-of-fit test, the minimum expected frequency should generally be at least 5. However, if this isn't satisfied, you might need to combine that category with a neighboring one, or use a different testing method that can handle lower frequencies, for instance, Fisher's exact test or the likelihood ratio test.

Step by step solution

01

Understanding Goodness-of-Fit Test

In a goodness of fit test, we are checking if our observed data fits a particular distribution. The observed data are classified into various categories.
02

Managing Minimal Expected Frequencies

For each category in a goodness-of-fit test, the general rule of thumb is that the expected frequency should be at least 5. This is known as the Rule of Five.
03

Alternatives When Condition is Not Satisfied

If this condition is not satisfied, that is, if the expected frequency in any category is less than 5, we may need to merge this category with an adjacent one, or try a different test, which can handle low frequencies, such as Fisher's exact test or the likelihood ratio test.

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